Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

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• 作者：Wensheng Tang^a ; ^{tangws@lsec.cc.ac.cn} ; Yajuan Sun^b ; ^c ; ^{sunyj@lsec.cc.ac.cn} ; Wenjun Cai^d ; ^{wenjuncai1@gmail.com}
• 关键词：Discontinuous Galerkin method ; Hamiltonian systems ; Continuous-stage PRK method ; Symplectic PRK scheme ; Multi-symplectic PRK scheme ; Conservation laws
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：340-364
• 全文大小：3399 K
• 卷排序：330

文摘

In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.